If you are pushing on block m1, I assume the other blocks are in front of it; otherwise m2 and m3 would be left behind and the solution would be trivial
(a1 = F/m1 and a2 = a3 = 0).
Therefore I would assume that
a1 = F/(m1 + m2 + m3)

The other blocks, being in front of m1, would accelerate at the same rate.

For the contact force, start with block m3, for which you know the acceleration AND the mass. use F3 = a3/m3 = a1/m3

Force F3 acts backwards on m2, and another force F2 acts forwards on it. Use that fact and a FBD to solve for F2.

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